Question

Помогите пожалуйста с логарифмами!

Answer 1

Ответ:

$1) log_{0.2}( log_{2}(32) ) = log_{0.2}(5) = log_{ {5}^{ - 1} }(5) = - log_{5}(5) = - 1$

$2) log_{ {13}^{2} }(13) - log_{3}( {3}^{ - 4} ) + 9 log_{3}( {3}^{ \frac{1}{3} } ) = \frac{1}{2} log_{13}(13) + 4 log_{13}(13) + 9 \times \frac{1}{3} log_{3}(3) = 0.5 + 4 + 3 = 7.5$

$3) log_{12}(16 \times 9) = log_{12}(144) = 2$

$4) log_{7}( \frac{147}{3} ) = log_{7}(49) = 2$

$5) \frac{ log_{c}(a) }{ log_{c}(b) } = log_{b}(a) \\ log_{2}(128) = 7$

$7)64 \times {64}^{ - log_{4}(6) } = 64 \times {4}^{ - 3 log_{4}(6) } = 64 \times {4}^{ log_{4}( \frac{1}{216} ) } = 64 \times \frac{1}{216} = \frac{16}{54} = \frac{8}{27}$

$8) {13}^{ \frac{3}{ log_{10}(13) } } = {13}^{3 log_{13}(10) } = {13}^{ log_{13}( {10}^{3} ) } = {10}^{3} = 1000$

$6) {5}^{ log_{5}( {10}^{4} ) } = {5}^{ log_{5}(10000) } = 10000$

Answer 2

Ответ:

Объяснение:

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